Fix tabs briefly animating too wide after finishing closing some tabs (ver. 2)

[petemill]

This PR replaces #12567 (and contains the revert from #12718)

Fix #12566

Since each tab's 'fixed width' was being removed at the same time, each one was measuring the width whilst other tab(s) were / were not reset back to a fluid width, causing measurements to be off.
Flex supports transitions / animations by default, so we do not need to measure the element ourselves in this case, anyway.
Also prevents pinned tabs from fixing tab width and prevents fixing tab width when tab page remains full.

Submitter Checklist:

• Submitted a ticket for my issue if one did not already exist.
• Used Github auto-closing keywords in the commit message.
• Added/updated tests for this change (for new code or code which already has tests).
• Ran git rebase -i to squash commits (if needed).
• Tagged reviewers and labelled the pull request as needed.
• Request a security/privacy review as needed. (Ask a Brave employee to help if you cannot access this document.)

Test Plan:

Reviewer Checklist:

• Request a security/privacy review as needed if one was not already requested.

Tests

• Adequate test coverage exists to prevent regressions
• Tests should be independent and work correctly when run individually or as a suite ref
• New files have MPL2 license header

[cezaraugusto]

++